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Firstly, the control panel area is extracted in the workspace of the HFM, in which the interacting point is located. Then a feasible interacting configuration is calculated as the objective configuration of the trajectory encoded by a parametric representation. The trajectory planning problem is formulated as a non-linear optimization problem based on kinematics, which is solved in real-time by finding a good initial solution with machine learning methods. Simulations show that trajectories with a compromise between safety and rapidity can be calculated in real-time by this method, which provides a basis for haptic interaction in VCSs.<\/jats:p>","DOI":"10.1177\/0037549718815755","type":"journal-article","created":{"date-parts":[[2019,6,5]],"date-time":"2019-06-05T10:16:15Z","timestamp":1559729775000},"page":"621-635","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Real-time kinematical optimal trajectory planning for haptic feedback manipulators"],"prefix":"10.1177","volume":"95","author":[{"given":"Shiyu","family":"Zhang","sequence":"first","affiliation":[{"name":"State Key Laboratory of Virtual Reality Technology and Systems, Beihang University, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuling","family":"Dai","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Virtual Reality Technology and Systems, Beihang University, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2019,6,5]]},"reference":[{"key":"bibr1-0037549718815755","first-page":"488","volume":"14","author":"Dai S","year":"2002","journal-title":"J Syst Simulat"},{"key":"bibr2-0037549718815755","first-page":"881","volume":"28","author":"Wang D","year":"2016","journal-title":"J Comput Aid Des Comput Graphic"},{"key":"bibr3-0037549718815755","volume-title":"Semi-virtual reality cockpit technology research based on data glove","author":"Yu T.","year":"2008"},{"key":"bibr4-0037549718815755","volume-title":"Research on key technologies for augmented semi-virtual reality cockpit","author":"Tang Y.","year":"2012"},{"key":"bibr5-0037549718815755","unstructured":"CGSD. 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